Problem: A circle has a circumference of ${12}$. It has an arc of length $11$. What is the central angle of the arc, in degrees?
The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{\theta}}{360^\circ} = {11} \div {12}$ $\dfrac{{\theta}}{360^\circ} = \dfrac{11}{12}$ ${\theta} = \dfrac{11}{12} \times 360^\circ$ ${\theta} = 330^\circ$ ${12}$ ${11}$ ${330^\circ}$